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Answered on 18 Apr Learn Sphere
Nazia Khanum
Problem Analysis:
Solution:
Determine Area Covered by Each Revolution:
Calculate Total Area Covered:
Convert Area to Square Meters:
Determine Cost of Levelling:
Final Calculation:
Detailed Calculation:
Final Answer:
The cost of levelling the playground at Rs. 2 per square meter is Rs. [insert calculated value].
Answered on 18 Apr Learn Sphere
Nazia Khanum
To find the cost of the cloth required to make a conical tent, we'll need to:
Solution:
Step 1: Calculate Slant Height (l)
Given:
Using Pythagoras theorem, we can find the slant height (l) of the cone: l=r2+h2l=r2+h2
l=72+242l=72+242
l=49+576l=49+576 l=625l=625
l=25 ml=25m
Step 2: Find Total Surface Area of the Tent
Total surface area (A) of a cone is given by: A=πr(r+l)A=πr(r+l)
A=π×7×(7+25)A=π×7×(7+25) A=π×7×32A=π×7×32 A≈704 m2A≈704m2
Step 3: Determine Length of Cloth Required
Given:
The length of cloth required will be equal to the circumference of the base of the cone, which is: C=2πrC=2πr
C=2π×7C=2π×7 C≈44 mC≈44m
Step 4: Calculate Cost of Cloth
Given:
The cost of cloth required will be: Cost=Length of cloth required×Rate of clothCost=Length of cloth required×Rate of cloth
Cost=44×50Cost=44×50 Cost=Rs.2200Cost=Rs.2200
Conclusion:
The cost of the 5 m wide cloth required at the rate of Rs. 50 per metre is Rs. 2200.
Answered on 18 Apr Learn Sphere
Nazia Khanum
Calculate the number of lead balls that can be made from a sphere of radius 8 cm, with each ball having a radius of 1 cm.
Solution:
Step 1: Calculate Volume of Sphere
Step 2: Calculate Volume of Each Lead Ball
Step 3: Determine Number of Lead Balls
Step 4: Conclusion
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Answered on 18 Apr Learn Real Numbers
Nazia Khanum
Adding Radical Expressions
Introduction: In mathematics, adding radical expressions involves combining like terms to simplify the expression. Radical expressions contain radicals, which are expressions that include square roots, cube roots, etc.
Problem Statement: Add 22+5322
+53 and 2−332−33
.
Solution: To add radical expressions, follow these steps:
Identify Like Terms:
and 22
and −33−33
Combine Like Terms:
Write the Result:
+53 and 2−332−33 is:
+23
Conclusion: The addition of 22+5322
+53 and 2−332−33 simplifies to 32+2332+23
.
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Introduction: In this problem, we are tasked with verifying whether the values x=2x=2 and y=1y=1 satisfy the linear equation 2x+3y=72x+3y=7.
Verification: We'll substitute the given values of xx and yy into the equation and check if it holds true.
Given Equation: 2x+3y=72x+3y=7
Substituting Given Values:
Solving the Equation: 4+3=74+3=7 7=77=7
Conclusion:
Therefore, the given values x=2x=2 and y=1y=1 indeed satisfy the linear equation 2x+3y=72x+3y=7.
Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Graph of 9x – 5y + 160 = 0
To graph the equation 9x – 5y + 160 = 0, we'll first rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Rewrite the equation in slope-intercept form
9x – 5y + 160 = 0
Subtract 9x from both sides:
-5y = -9x - 160
Divide both sides by -5 to isolate y:
y = (9/5)x + 32
Now we have the equation in slope-intercept form.
Step 2: Identify the slope and y-intercept
The slope (m) is 9/5 and the y-intercept (b) is 32.
Step 3: Plot the y-intercept and use the slope to find additional points
Now, let's plot the y-intercept at (0, 32). From there, we'll use the slope to find another point. The slope of 9/5 means that for every 5 units we move to the right along the x-axis, we move 9 units upwards along the y-axis.
So, starting from (0, 32), if we move 5 units to the right, we move 9 units up to get the next point.
Step 4: Plot the points and draw the line
Plot the y-intercept at (0, 32) and the next point at (5, 41). Then, draw a line through these points to represent the graph of the equation.
Finding the value of y when x = 5
To find the value of y when x = 5, we'll substitute x = 5 into the equation and solve for y.
9x – 5y + 160 = 0
9(5) – 5y + 160 = 0
45 – 5y + 160 = 0
Combine like terms:
-5y + 205 = 0
Subtract 205 from both sides:
-5y = -205
Divide both sides by -5 to solve for y:
y = 41
So, when x = 5, y = 41.
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Answered on 18 Apr Learn Linear equations in 2 variables
Nazia Khanum
Finding Solutions of Line AB Equation
Given Information:
Procedure:
1. Identify Points on Line AB:
2. Determine Coordinates:
3. Substitute Coordinates:
4. Verify Solutions:
Example:
Conclusion:
Answered on 18 Apr Learn Polynomials
Nazia Khanum
Determining the Value of k
Introduction: To find the value of k when (x – 1) is a factor of the polynomial 4x^3 + 3x^2 – 4x + k, we'll utilize the Factor Theorem.
Factor Theorem: If (x – c) is a factor of a polynomial, then substituting c into the polynomial should result in zero.
Procedure:
Step-by-Step Solution:
Substitute x=1x=1:
Solve for k:
Conclusion: The value of k when (x – 1) is a factor of the given polynomial is k=−3k=−3.
Answered on 18 Apr Learn Polynomials
Nazia Khanum
Solution: Finding Values of a and b
Given Problem: If x3+ax2–bx+10x3+ax2–bx+10 is divisible by x2–3x+2x2–3x+2, we need to find the values of aa and bb.
Solution Steps:
Step 1: Determine the factors of the divisor
Given divisor: x2–3x+2x2–3x+2
We need to find two numbers that multiply to 22 and add up to −3−3.
The factors of 22 are 11 and 22.
So, the factors that add up to −3−3 are −2−2 and −1−1.
Hence, the divisor factors are (x–2)(x–2) and (x–1)(x–1).
So, the divisor can be written as (x–2)(x–1)(x–2)(x–1).
Step 2: Use Remainder Theorem
If f(x)=x3+ax2–bx+10f(x)=x3+ax2–bx+10 is divisible by (x–2)(x–1)(x–2)(x–1), then the remainder when f(x)f(x) is divided by x2–3x+2x2–3x+2 is zero.
According to Remainder Theorem, if f(x)f(x) is divided by x2–3x+2x2–3x+2, then the remainder is given by f(2)f(2) and f(1)f(1) respectively.
Step 3: Find the value of aa
Substitute x=2x=2 into f(x)f(x) and equate it to 00 to find the value of aa.
f(2)=23+a(2)2–b(2)+10f(2)=23+a(2)2–b(2)+10
0=8+4a–2b+100=8+4a–2b+10
18=4a–2b18=4a–2b
4a–2b=184a–2b=18
Step 4: Find the value of bb
Substitute x=1x=1 into f(x)f(x) and equate it to 00 to find the value of bb.
f(1)=13+a(1)2–b(1)+10f(1)=13+a(1)2–b(1)+10
0=1+a–b+100=1+a–b+10
11=a–b11=a–b
a–b=11a–b=11
Step 5: Solve the equations
Now we have two equations:
We can solve these equations simultaneously to find the values of aa and bb.
Step 6: Solve the equations
Equation 1: 4a–2b=184a–2b=18
Divide by 2: 2a–b=92a–b=9
Equation 2: a–b=11a–b=11
Step 7: Solve the system of equations
Adding equation 2 to equation 1: (2a–b)+(a–b)=9+11(2a–b)+(a–b)=9+11
3a=203a=20
a=203a=320
Substitute a=203a=320 into equation 2: 203–b=11320–b=11
b=203–11b=320–11
b=20–333b=320–33
b=−133b=3−13
Step 8: Final values of aa and bb
a=203a=320
b=−133b=3−13
So, the values of aa and bb are a=203a=320 and b=−133b=3−13 respectively.
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Answered on 18 Apr Learn Polynomials
Nazia Khanum
Monomial and Binomial Examples with Degrees
Monomial Example (Degree: 82)
Binomial Example (Degree: 99)
Additional Notes:
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